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How to Perform Welch's t-Test in Python
Calculate the Welch t-statistic and degrees of freedom for two samples with unequal variances using Python's statistics module.
import math
from statistics import mean, variance
def welch_t_test(sample1, sample2):
n1, n2 = len(sample1), len(sample2)
mean1, mean2 = mean(sample1), mean(sample2)
var1, var2 = variance(sample1), variance(sample2)
# Welch's t statistic
t_stat = (mean1 - mean2) / math.sqrt(var1 / n1 + var2 / n2…How to Run a Fisher Exact Test in Python
Compute the two-sided Fisher exact test p-value for a 2x2 contingency table using pure Python and the math module.
from math import comb, factorial
from itertools import combinations
def hypergeometric_probability(a, b, c, d):
"""Probability of observing table [[a, b], [c, d]] under the null."""
row1 = a + b
row2 = c + d
col1 = a + c
col2 = b + d
total = row1 + row2
return (comb(row1, a) * comb(row2, …How to Run a Permutation Test in Python
Run a Monte Carlo permutation test to compute a p-value for comparing two group means without parametric assumptions.
import random
import statistics
def permutation_test(group_a, group_b, n_permutations=10000, seed=42):
random.seed(seed)
combined = group_a + group_b
observed_diff = abs(statistics.mean(group_a) - statistics.mean(group_b))
count = 0
n = len(group_a)
for _ in range(n_permutations):
…How to Simulate Geo Experiments in Python
Build a mock geo experiment simulator with ramp-up/down periods, measuring weekly lift between treatment and control markets.
import random
import math
from dataclasses import dataclass
@dataclass
class GeoMarket:
name: str
base_demand: float
geo_coefficient: float
def simulate_geo_experiment(markets, weeks=12, control_weeks=6):
"""
Simulates a geo experiment with ramp-up and ramp-down periods.
Returns weekly lift p…How to join assignment logs with outcomes in Python
Merge submission log entries with grading outcomes using left join and full outer join patterns in pure Python.
from datetime import datetime, timedelta
class AssignmentLog:
def __init__(self):
self.logs = [
{"assignment_id": 101, "student_id": "S001", "submitted_at": "2024-03-01 10:30:00"},
{"assignment_id": 101, "student_id": "S002", "submitted_at": "2024-03-02 14:15:00"},
{"as…How to simulate a contextual bandit in Python
Simulate a contextual multi-armed bandit with random features and epsilon-greedy action selection in Python.
import random
class ContextualBandit:
def __init__(self, n_actions=3, n_features=4):
self.n_actions = n_actions
self.n_features = n_features
self.theta = [random.random() for _ in range(n_actions * n_features)]
def mock_context(self):
return [random.uniform(-1, 1) for _ in ra…Synthetic Control in Python: Mock Example
Implements synthetic control from scratch: learns donor weights via ridge regression on pre-period data, then predicts a counterfactual for the treated unit.
import numpy as np
class SyntheticControl:
def __init__(self, data, treated_index, pre_periods, post_periods):
self.data = np.array(data, dtype=float)
self.treated_index = treated_index
self.pre_periods = pre_periods
self.post_periods = post_periods
def fit_weights(sel…Thompson Sampling Mock Bandit in Python
Implement a Thompson sampling multi-armed bandit to explore and exploit reward probabilities across multiple options, updating Beta distributions over time.
import random
class ThompsonSamplingBandit:
def __init__(self, num_arms, alpha=1.0, beta=1.0):
self.num_arms = num_arms
self.alpha = [alpha] * num_arms
self.beta = [beta] * num_arms
def select_arm(self):
samples = [random.betavariate(a, b) for a, b in zip(self.alpha, self.beta…UCB1 Bandit Algorithm in Python
This code implements the UCB1 multi-armed bandit algorithm, balancing exploration and exploitation to identify the best arm while maximizing cumulative reward.
import math
import random
def ucb1(means, n_iterations=1000, exploration_weight=2.0):
"""Run UCB1 bandit algorithm on arms with given true means."""
n_arms = len(means)
counts = [0] * n_arms
rewards = [0.0] * n_arms
for t in range(1, n_iterations + 1):
# UCB1 selection
if t <…Approximate Count with HyperLogLog in Python
A mock HyperLogLog implementation uses hash-based registers to estimate cardinality of large datasets with sublinear memory.
import hashlib
class HyperLogLog:
def __init__(self, precision=4):
if precision < 4 or precision > 16:
raise ValueError("precision must be between 4 and 16")
self.precision = precision
self.registers = [0] * (1 << precision)
def _hash(self, value):
return int(hashl…Build a Full Text Search Index in Python
Create a simple inverted index for full-text search with the standard library, supporting multi-word AND queries across documents.
import re
from collections import defaultdict
class SimpleTextIndex:
def __init__(self):
self.index = defaultdict(list)
self.documents = {}
def add_document(self, doc_id, text):
self.documents[doc_id] = text
words = set(re.findall(r'\w+', text.lower()))
for word in wo…Composite index leftmost prefix in Python
Simulate a composite index in SQLite and check whether query columns match the leftmost prefix rule for index usage.
import sqlite3
def get_indexed_columns(table_name):
"""Simulate a composite index by reading column names that start with 'idx_'."""
conn = sqlite3.connect(":memory:")
conn.execute(f"CREATE TABLE {table_name} (id INTEGER, idx_col1 TEXT, idx_col2 INTEGER, other TEXT)")
conn.execute(f"CREATE INDEX idx_…Consistent Hashing with Virtual Buckets in Python
This code maps many virtual buckets onto a few physical buckets using a consistent hashing ring, ensuring balanced distribution with minimal remapping when physical buckets change.
import random
class VirtualBuckets:
"""Maps many virtual buckets onto few physical buckets using consistent hashing."""
def __init__(self, physical_buckets, virtual_factor=100):
self.physical = list(physical_buckets)
self.virtual_factor = virtual_factor
self.ring = []
self…Cross Shard Query Scatter Gather Mock in Python
Simulate a distributed database cross-shard query using a scatter-gather pattern with a mock Python implementation.
from dataclasses import dataclass
from typing import List, Dict
@dataclass
class NodeResponse:
node_id: int
data: Dict[str, float]
def mock_query_shard(shard_id: int, shard_data: Dict[str, float], query: str) -> NodeResponse:
"""Simulate querying a single shard, returning matches whose value > 50."""
…Database Helper in Python with SQLite Scaling Optimization
Build a beginner-friendly SQLite database helper class with WAL, indexed queries, and efficient batch inserts for scaling.
import sqlite3
from contextlib import contextmanager
class DatabaseHelper:
"""Beginner-friendly helper for SQLite database operations with scaling tips."""
def __init__(self, db_path):
self.db_path = db_path
@contextmanager
def connection(self):
"""Context manager for automatic comm…How to Build a Connection Pool Reuse Mock in Python
Build a mock connection pool with context manager to track connection reuse, acquires, and releases in Python.
import time
from contextlib import contextmanager
class Connection:
def __init__(self, name):
self.name = name
self.in_use = False
self.busy_since = None
def fetch(self):
return f"data from {self.name}"
class ConnectionPool:
def __init__(self, size=3):
self.conn…How to Build a Shard Map Mock Dict in Python
Implement a dictionary-like class that distributes keys across multiple shards using Python's hash() for realistic data partitioning.
class ShardMap:
def __init__(self, shard_count):
self.shards = {i: {} for i in range(shard_count)}
self.shard_count = shard_count
def _shard_for(self, key):
return hash(key) % self.shard_count
def __getitem__(self, key):
return self.shards[self._shard_for(key)][key]
d…How to Create a Covering Index with INCLUDE Columns in Python
Create a covering index with INCLUDE columns in SQLite from Python and inspect the query plan to confirm the index covers the query.
import sqlite3
def create_covering_index_mock():
conn = sqlite3.connect(":memory:")
cursor = conn.cursor()
cursor.execute("""
CREATE TABLE employees (
id INTEGER PRIMARY KEY,
name TEXT,
department TEXT,
salary INTEGER
)
""")
employe…How to Eager Load with JOIN to Reduce N+1 Queries in Python
Demonstrates eager loading with a SQL JOIN to reduce N+1 query patterns down to a single database call when fetching related data.
import sqlite3
def eager_load_join_reduce(mock_db_path=":memory:"):
"""Demonstrate eager loading where joins reduce query count from N+1 to 1."""
conn = sqlite3.connect(mock_db_path)
cursor = conn.cursor()
cursor.executescript(
"""
CREATE TABLE authors (id INTEGER PRIMARY KEY, name TE…How to Explain SQLite Query Plans in Python
Build a Python function that runs EXPLAIN QUERY PLAN on SQLite in-memory tables and prints the optimizer's execution plan for any SELECT statement.
import sqlite3
def explain_query(sql: str) -> str:
"""Return the SQLite query plan for the given SQL statement."""
conn = sqlite3.connect(":memory:")
cursor = conn.cursor()
# Create sample data for a realistic plan
cursor.execute("CREATE TABLE users (id INTEGER PRIMARY KEY, name TEXT)")
c…How to Implement Consistent Hashing in Python
Build a consistent hash ring in Python that distributes keys across nodes and minimizes remapping when nodes are added or removed.
import hashlib
from bisect import bisect_right
class ConsistentHashRing:
def __init__(self, nodes, replicas=3):
self.replicas = replicas
self.ring = {}
self.sorted_keys = []
for node in nodes:
self.add_node(node)
def _hash(self, key):
return int(hashlib.md…How to Implement Keyset Pagination in Python (Seek Method)
Implement keyset (seek) pagination in Python with a mock paginator that efficiently fetches pages based on the last row rather than OFFSET.
from dataclasses import dataclass
from typing import List, Optional
@dataclass
class Row:
id: int
name: str
def __lt__(self, other: "Row") -> bool:
return (self.id, self.name) < (other.id, other.name)
class MockKeysetPaginator:
"""Pagination using keyset (seek) method instead of OFFSET."""…How to Implement Read-After-Write Consistency Mock in Python
Simulate strong versus eventual read-after-write consistency with a primary and replica store, demonstrating the difference in data visibility over time.
import time
class MockStorage:
def __init__(self, write_delay=0.1):
self.store = {}
self.replica = {}
self.write_delay = write_delay
def write(self, key, value):
# Write to primary storage immediately
self.store[key] = value
# Simulate async replication delay
…How to Mock SQLite executemany When Batch Inserting in Python
Batch insert many rows into SQLite with executemany and mock the cursor for isolated tests.
import sqlite3
from unittest.mock import Mock, patch
def insert_users(conn, users):
"""Insert multiple user records using executemany."""
cursor = conn.cursor()
cursor.executemany(
"INSERT INTO users (name, age) VALUES (?, ?)",
users
)
conn.commit()
return cursor.rowcount
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